Lane-Emden equations of second kind modelling thermal explosion in infinite cylinder and sphere  

作　　者：K.REGER R.A.VAN GORDER 

机构地区：[1]Department of Mathematics,University of Central Florida

出　　处：《Applied Mathematics and Mechanics(English Edition)》2013年第12期1439-1452,共14页应用数学和力学（英文版）

基　　金：supported by the National Science Foundation of U.S.A.(No.1144246)

摘　　要：We study a modified version of the Lane-Emden equation of the second kind modelling a thermal explosion in an infinite cylinder and a sphere. We first show that the solution to the relevant boundary value problem is bounded and that the solutions are monotone decreasing. The upper bound, the value of the solution at zero, can be approximated analytically in terms of the physical parameters. We obtain solutions to the boundary value problem, using both the Taylor series （which work well for weak nonlinearity） and the b-expansion method （valid for strong nonlinearity）. From here, we are able to deduce the qualitative behavior of the solution profiles with a change in any one of the physical parameters.We study a modified version of the Lane-Emden equation of the second kind modelling a thermal explosion in an infinite cylinder and a sphere. We first show that the solution to the relevant boundary value problem is bounded and that the solutions are monotone decreasing. The upper bound, the value of the solution at zero, can be approximated analytically in terms of the physical parameters. We obtain solutions to the boundary value problem, using both the Taylor series （which work well for weak nonlinearity） and the b-expansion method （valid for strong nonlinearity）. From here, we are able to deduce the qualitative behavior of the solution profiles with a change in any one of the physical parameters.

关 键 词：Lane-Emden equation BIFURCATION thermal explosion analytical method 

分 类 号：O302[理学—力学]